Chpt 13 Flashcards
What does ANOVA stand for
Analysis of Variance
what is the F- ratio
is the ratio of 2 variables
What does ANOVA allow us to do?
allows us to compare multiple pops and even subgroups of these pops
- how two groups interact with each other quantitatively
What question does ANOVA help us answer
do all 3 means come form a common population
- we are not asking if they were exactly equal. we are asking if each mean likely came from the larger overall population
What is the Null hypothesis for ANOVA
HO= M1 = M2 = M3
What is the problem with using pairwise comparison for 3 pop means
the type I error will compound with each t-test
95% confidence = (.95)(.95)(.95) = .857
so, a (or critical value) would be come 1 - .857 =
143
Type 1 error rate went from 5% (0.05) to 14.3%
what is partitioning
separating total variance into its component parts
- we do this by using ANOVA
What is the variability between the means
distance from overall mean
if the variability between the means (distance from overall mean) in the numerator is relatively Large compared to the variance within the samples the ratio will be
much larger than 1
- the samples mostly likely do NOT come from a common pop
- reject Ho that means are equal
What is the variability within the samples called
internal spread (the denominator)
If the F ratio is similar/similar what does this tell us
- Fail to reject Ho
- means are fairly close to overall mean and/ or distributions overlap a bit
If the F ratio is Small /Large
- Fail to reject Ho
- the means are very close to overall mean and/or distributions melt together
What is the formula for f ratio
B/W / W/in or Among / Around
variance b/w + Variance w/in (error variance) =
Total variance
Factor definition
independent variable (ie. assembly method)
What are the required assumptions for ANOVA
- normally distributed
- distributions must be independent
- the variance of the response variable (Qsquared) is the same for all pops
What are the steps to ANOVA
- Calculate sample mean for each pop
- calculate overall mean for all pops (add up all means / # of means)
- Estimate the variance (Xbar 1- Overall mean)squared / n-1
- compute the sum of squares b/w treatments
- computer mean squares b/w treatments
- calculate sum of squares due to error
- calculate the mean squares due to error
- Setup the ANova table
- calculate f-ratio and p-value
what is SSTR stand for
sum of squares b/w treatments
what is MSTR
mean square b/w treatments
what is SSE
sum of squares due to error
What is MSE
mean square due to error
what is the formula for SSTR
sum (# of sample)(pop1 mean - overall mean)sqaured (do for each set of pops)
What is the formula for MSTR
SSTR/k-1
What is the formula for SSE
(# of samples)(Variance of pop1) + (# of samples) (Variance of pop2) + (# of samples)(Variance of Pop3)